Finite Group DatabasebetaFinite Group Databasebeta| order | 26668 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#90673 |
| Fitting, socle, Hall | C59×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #90673 |
| commutator, hypocenter | C113 | C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C59×C113 | C4 |
| prime radical | C59×D113 | C2 |
| cosocle | D113 | C2×C59 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C59 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6667 |
1888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26668, 6);